17 ideas
21642 | If quantification is all substitutional, there is no ontology [Quine] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
1633 | Absolute ontological questions are meaningless, because the answers are circular definitions [Quine] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
18964 | Ontology is relative to both a background theory and a translation manual [Quine] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
18965 | We know what things are by distinguishing them, so identity is part of ontology [Quine] |
1634 | Two things are relative - the background theory, and translating the object theory into the background theory [Quine] |
8470 | Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein] |
18963 | Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine] |